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The Problem of Catalan (Hardcover, 2014 ed.)
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The Problem of Catalan (Hardcover, 2014 ed.)
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In 1842 the Belgian mathematician Eugene Charles Catalan asked
whether 8 and 9 are the only consecutive pure powers of non-zero
integers. 160 years after, the question was answered affirmatively
by the Swiss mathematician of Romanian origin Preda Mihailescu. In
other words, 32 - 23 = 1 is the only solution of the equation xp -
yq = 1 in integers x, y, p, q with xy 0 and p, q 2. In this book we
give a complete and (almost) self-contained exposition of
Mihailescu's work, which must be understandable by a curious
university student, not necessarily specializing in Number Theory.
We assume a very modest background:a standard university course of
algebra, including basic Galois theory, and working knowledge of
basic algebraic number theory.
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